Tim Wescott wrote:> On Thu, 22 Oct 2009 04:54:12 -0500, lagoule wrote: > >> Hello, >> >> I'm working on a monitoring project of a three-phase power system, which >> means my inputs are three sinusoïdal of 60Hz with 60 degres phase >> difference between any two of them. Of courses, these inputs also >> include noise and harmonics. >> >> I would like to actually measure the phase between the three signals, to >> make sure the 60 degres is there. Since it should be pretty accurate, I >> have to be able to measure very small difference between phases, in the >> tenth of degree. >> >> The problem is, I don't know if and how such a precision can be >> acheived. >> >> Under Matlab, I tried two different approach. The first one was to >> multiply each input with a reference sin and cos, lowpass the result and >> use arctan to get the phase in relation with my ref. The second was to >> use a Kalman filter to estimate the in-phase and quadrature-phase of the >> 60Hz present in the inputs. Then, the phase between two inputs is >> obtained by difference of their instantaneous phase. >> >> Both methods gave me noisy results, without the precision I require. So >> I was asking if you think the precision of 0.1 degree can be acheive and >> what would be the best way to measure the phase difference? > > So you took a couple of stabs at a theoretical problem with a practical > tool, and you didn't find joy. > > Maybe it's time to break out the pencil and paper? > > Assuming that you have good sampling and all the time in the world, it > should be trivial to get the information that you want from a long enough > sample set, and either of your approaches sound valid on their faces.I'm still curious. Is this an ordinary three-phase system with phases equally spaced (120 degreed apart) or is one of the phases inverted? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Three-phase power: Phase Estimation
Started by ●October 22, 2009
Reply by ●October 24, 20092009-10-24
Reply by ●October 24, 20092009-10-24
On Sat, 24 Oct 2009 11:48:53 -0400, Jerry Avins wrote:> Tim Wescott wrote: >> On Thu, 22 Oct 2009 11:57:22 -0400, Jerry Avins wrote: >> >>> lagoule wrote: >>>> Hello, >>>> >>>> I'm working on a monitoring project of a three-phase power system, >>>> which means my inputs are three sinusoïdal of 60Hz with 60 degres >>>> phase difference between any two of them. >>> A very unusual system! In most, the phases are 360/3 =120 degrees >>> apart. >>> >>>> Of course, these inputs also include noise and >>>> harmonics. >>>> >>>> I would like to actually measure the phase between the three signals, >>>> to make sure the 60 degres is there. Since it should be pretty >>>> accurate, I have to be able to measure very small difference between >>>> phases, in the tenth of degree. >>>> >>>> The problem is, I don't know if and how such a precision can be >>>> acheived. >>>> >>>> Under Matlab, I tried two different approach. The first one was to >>>> multiply each input with a reference sin and cos, lowpass the result >>>> and use arctan to get the phase in relation with my ref. The second >>>> was to use a Kalman filter to estimate the in-phase and >>>> quadrature-phase of the 60Hz present in the inputs. Then, the phase >>>> between two inputs is obtained by difference of their instantaneous >>>> phase. >>>> >>>> Both methods gave me noisy results, without the precision I require. >>>> So I was asking if you think the precision of 0.1 degree can be >>>> acheive and what would be the best way to measure the phase >>>> difference? >>> Can you use a linear-phase narrow filter around 60 Hz to remove the >>> perturbations from noise and harmonics? That should work if latency >>> isn't a problem. >>> >>> If the phases are balanced and you really have them at 0, 60, and 120 >>> degrees, invert the one at 60, moving it to 240. Then the all >>> harmonics not divisible by 3 will cancel in the sum. Residual 60 Hz >>> will indicate either amplitude imbalance or phase shift. >>> >>> Jerry >> >> But _no_ residual 60Hz will _either_ indicate no amplitude imbalance or >> phase shift, or _both_ amplitude imbalance _and_ phase shift. > > I don't intend to go through the math, but I can't off hand see those > errors canceling. That makes no sense, but in practice: Show mw. > > JerryWell, a degenerate case is one where you have one signal at 0 degrees and full amplitude, and two signals each at 180 degrees and half amplitude. Sum = 0. You can find the amplitude and phase of the sum of any two signals; just do that, invert the phase, specify it as your third signal and voilein! (that's a small voile, by the way) you have your answer. -- www.wescottdesign.com
Reply by ●October 24, 20092009-10-24
On Oct 22, 2:54 am, "lagoule" <zegh...@gmail.com> wrote:> Hello, > > I'm working on a monitoring project of a three-phase power system, which > means my inputs are three sinuso�dal of 60Hz with 60 degres phase > difference between any two of them. Of courses, these inputs also include > noise and harmonics. > ... > Jonathan Drolet > �cole Polytechnique de Montr�alTake a look at: "Digital Measurement of Phase Difference - A Comparative Study of DSP Algorithms" at: http://www.metrology.pg.gda.pl/full/2005/M&MS_2005_427.pdf "The paper compares nine methods..." Dale B. Dalrymple
